兩類波動方程的導數(shù)損失問題的研究.pdf

1、西南交通大學碩士學位論文兩類波動方程的導數(shù)損失問題的研究姓名：王偉申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：楊晗20120510西南交通大學碩士研究生學位論文第1I頁AbstractInthisthesis，theCauchyproblemforwaveequationswithvariablecoefficientsinthetimevariableisconsideredUndersomeappropriateconditionso

2、nthecoefficientsa(t)，byestablishingtheestimatesoftheenergyfunctional，thelossofderivativestothesolutionfortheCauchyproblemisobtainedThemainresultsofthisthesisarestatedasfollows(1)Thec。efficient口(f)satis觚thecondition№)B號謝t

3、ll，∈【o，1】forf∈(o，丁】，If，∈【o，1)，thenthereisnolossofderivatives，thatis，theenergyinequalityE(材)(f)≤e巨(材)(o)holdsfors≥0；If，=l，thenthereisafinitelossofderivatives，thatis，theenergyinequalityE一知(甜)(，)≤e巨(”)(o)holdforlargeswithap

4、ositiveconstantS0(2)Thecoefficienta(t)satisfieswithl吼(Hf)一q(，)IO，Iv[0，thesolutionoftheCauchyproblemforwaveequationsatisfiesE一艿(z，)(f)≤GE(Ⅳ)(o)，Go，f∈(o，計KeyWords：Waveequation；Cauchyproblem；Lossofderivatives；Gronwallinequa